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Q.

In Figure, a block of mass 4 kg falls on a spring from a height 15 cm. If the spring constant of spring is 2000 N/m, maximum compression in the spring will be : (take g = 10 m/s²)

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a

18.2 cm

b

12.6 cm

c

14 cm

d

10 cm

answer is D.

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Detailed Solution

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At the maximum compression (x_m)velocity of block = 0
Now from work- Energy Theorem $W = ΔKE$
$mg (15 \times 10^{- 2} + x_{m}) - \frac{1}{2} {kx}_{m}^{2} = 0 - 0$
$\Rightarrow 4 (10) (0 .15 + x_{m}) - \frac{1}{2} (2000) x_{m}^{2} = 0$
$\Rightarrow 1000 x_{m}^{2} - 40 x_{m} - 6 = 0$
X_m = 0.10 m

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In Figure, a block of mass 4 kg falls on a spring from a height 15 cm. If the spring constant of spring is 2000 N/m, maximum compression in the spring will be : (take g = 10 m/s2)